x(t) for constant acceleration

v(t) for constant acceleration

Average velocity

therefore

4 equations to use for constant acceleration phenomena (only)

4 equations to use for constant acceleration phenomena (only)

Variables:

x x0

v v0

a t

If you know 4 (or sometimes 3) variables, you can solve for the other variables.

Constant Acceleration (Problem Solving)

1. Identify the “main idea” of the problem if it is readily apparent. For example, “constant acceleration.”

2. Draw pictures, label objects, write knowns and unknowns. Use subscripts with variables if there are multiple objects in the problem.

3. Write physics equations, definitions, and laws that might help solve the problem.

4. Do the math.

5. Check your work. Does the answer make sense?

Example

A softball player is running at full speed toward second base with a speed of 12 m/s. She slides for 1.5 m into second base. Assuming constant acceleration, (1) how much time elapses as she is sliding; and (2) What is her acceleration?

Example

Motorcycles have amazing acceleration. The Kawasaki Ninja ZX-14 can reportedly accelerate from 0 to 60 mph in 2.5 s. What is its acceleration and how far does it travel during this time interval?

Free-fall

An “free” object rising or falling near Earth, with negligible air resistance, is a special case of motion with constant acceleration.

+y (m)

Equations of motion for free-fall

Example

A diver steps off a 10-m platform. If she starts from rest (approximately) at t=0, how fast is she moving and what is the clock reading when she hits the water?

Example

A tennis player is working on his serve. He wants to toss the tennis ball vertically exactly 1.5 m above where the ball leaves his hand. With what speed must the ball leave his hand?

Example

A batter hits a pop-fly that travels straight upward and is ultimately caught by the catcher. (a) If the speed of the ball after colliding with the bat is 30 m/s, what maximum height (above the bat) will the ball travel? (b) What is the velocity of the ball when it is caught by the catcher?